In Millikan's oil drop experiment an oil drop of radius `r` and change `Q` is held in equilibrium between the plates of a charged parallel plate capacitor when the potential change is `V`. To keep a drop radius `2r` and with a change `2Q` is equilibriu between the plates the potential difference `V'` required is:

Options

A. `V`
B. `2V`
C. `4V`
D. `8V`

Answer

C

Explanation

In Millikan's oil drop experiment,
`qE = Mg`
Here `R = (v)/(d)` and `M = (4)/(3) pi r^(3) rho`
`:. (qV)/(d) = (4)/(3) pi r^(3) rho g`
or `V = ((d)/(q)) (4)/(3) pi r^(3) rho g = ((r^(3))/(q)) ((4)/(3)pi rho d) g`
Fro second oil drop, `V' = [((2r)^(3))/(2q)][(4)/(3)pi rhod]g`
`:. (V')/(V) = 4` or `V' = 4V`